Axial-momentum analysis led to a power coefficient C P = 4a(1 a) 2 for a HAWT
Question:
Axial-momentum analysis led to a power coefficient CP = 4a(1 − a)2 for a HAWT eq. (30.7)
Compute the power coefficient another way: start from the tangential force per unit length f T in the simple model that led to eq. (30.12)
implement the axial momentum theory constraint (30.15)
find the torque per unit length dτ/dr R and compute the power
Show that the result is the same as the result of the axial-momentum analysis (30.7).
v4 = (1 – 2a)v1 v2 = (1 – a)v1, AT 1- 2a |A1 = (1 – a)AT, A4 %3| P = ;PoviAT4a(1 – a)² . Sr=-K Bu°ci sinø 2 pOK Bu²(1 – a)²c , 2. 2 sin o FN=PoK Bw?cj cos o âf = poK Bv²(1 – a)²cj cos ê, 2 sin? o
Step by Step Answer:
Combining the expression for f T from eq 3012 with the co...View the full answer
Related Video
In Physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. In this video, the concept of force and torque is demonstrated with the practical application of changing the flat tire of the car.
Students also viewed these Physics questions
-
Derive eq. (30.15) by equating the normal force per unit length on a blade element given in eq. (30.12) with the thrust per unit length obtained from the axial momentum analysis (30.14) . 8 K sin o c...
-
A variable-speed HAWT has a power coefficient of 0.45 at its rated wind speed v r and maintains its rated power for wind speeds between this value and its cutout speed of 25 m/s. If the rotor...
-
An economizer is to be purchased for a power plant. The unit is to be large enough to heat 7.5 kg/s of pressurized water from 71 to 182?C. There are 26 kg/s of flue gases (cp = 1000 J/(kg K))...
-
In Exercises 3344, use the graph of y = f(x) to graph each function g. g(x) = f(x) - 2 -4,0) -5-4-3 4-33 y = f(x) y (0,0) 2- 3.4 45 -2) (4-2) X
-
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of cross-linked cotton fabric. An increase in the degree of cross-linking, as...
-
A X2 test involving a 2 x 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-2. Using the claim and table in Example 4, verify that the X2 test...
-
Eager Beaver, Inc., started 2011 with total assets of \($24,000\) and total liabilities of \($11,000\). At the end of 2011, the businesss total assets stood at \($34,000\), and its total liabilities...
-
Using the information from C4-2 and assuming that the beginning budgetary and GAAP fund balance is $1,952,667, prepare the Statement of Revenues, Expenditures, and Changes in Fund BalanceBudget and...
-
The slashing in half of capital gains tax has made growth shares an attractive proposition. If you hold onto shares for more than 12 months before you sell them and you are on the top marginal tax...
-
Demand for Quiggly Pops follows an up and down pattern over the four quarters of a year, with peaks in the spring and winter months when special promotions are held. Production is handled by a highly...
-
Verify the results of eq. (30.7) and evaluate them at the Betz limit. v4 = (1 2a)v1, %3D v2 = (1 a)v1, 1- a AT, 1- 2a A4 A1 = (1 a)AT, 1 P = = ;pov{AT4a(1 a) .
-
The axial-momentum theory approximation to blade design breaks down when r/R becomes too small. Use eqs. (30.11) and (30.15) to show that the condition KB < 2r limits the angle to sin tan < c l (1...
-
Construct a truth table for the statement. (p ~ q) r
-
The following production data were taken from the records of the Finishing Department for June: Inventory in process, June 1 (32% completed) Completed units during June Ending inventory (65%...
-
Consider the statement: If demand curves are always downward-sloping and we have 4,000 units sold when we charged $20 for our product, then increasing our price to $25 will result in sales less than...
-
Submit a a 3C+Q response to the following case study in regards "Hazy Forecasts of Marijuana Tax Revenue in Washington State." Compliment: Connect: Comment: Question: In hindsight, how should the...
-
1. Solve the following linear systems. a. [x, y] = [1, 6]+s[3, -2] b. [x, y] [-12, -7]+s[8, -5] [x, y] [4, 4]+t[-6, 4] [x, y] [2, -1]+t[3, -2] C. [x, y] [16, 1]+s[5, 1] d. [x, y] [11, 12]+s[2,7] [x,...
-
Rough endoplasmic reticulum is characterized by what?
-
Inherited cancers like retinoblastoma show a dominant pattern of inheritance. However, the underlying genetic defect is a recessive loss-of-function mutationoften the result of a deletion. How can...
-
Based on the scenario described below, generate all possible association rules with values for confidence, support (for dependent), and lift. Submit your solutions in a Word document (name it...
-
Solve the following system of simultaneous equations by Gaussian elimination. x 1 + 4x 2 - 5x 3 = 4 3x 2 + 4x3 = -1 -2x 1 -1x 2 + 2x 3 = -3
-
Determine the solution of the following simultaneous equations by the inverse method. 1x 1 + 3x 2 = 5 4x 1 - 1x 2 = 12
-
Determine the solution of the following simultaneous equations by the inverse method. 1x 1 + 3x 2 = 5 4x 1 - 1x 2 = 12
-
Managers use CVP concepts to perform sensitivity analysis. Sensitivity analysis is a "what-if" technique that asks what will happen to a company's breakeven or target profit if sales price, costs, or...
-
John Fleming, chief administrator for Valley View Hospital, is concerned about the costs for tests in the hospital s lab. Charges for lab tests are consistently higher at Valley View than at other...
-
A company is looking at new equipment with an installed cost of $436,859. This cost will be depreciated straight-line to zero over the project's 6-year life, at the end of which the equipment can be...
Study smarter with the SolutionInn App